 Hello and welcome to the session. In this session we discuss the following question which says a certain amount of water is heated and the temperatures at different intervals of time were observed as follows. Draw a temperature time graph. Estimate the temperature of the water at t equal to 3.5 minutes. So this is the table of observations given to us. In this we have the time, that is small t in minutes, and the temperature, that is capital T, in deine C. So at one minute the temperature is 10 degrees C. At two minutes the temperature is 35 degrees C. At three minutes the temperature is 45 degrees C. At four minutes the temperature is 60 degrees C and at five minutes the temperature is 75 degrees C. we have to draw a temperature time graph. Let's start with the solution now. First of all we will take the time that is small t on the horizontal reference line and we take the temperature that is capital T on the vertical reference line. So we have shown this time that is in minutes on the horizontal reference line and the temperature that is capital T in degree Celsius on the vertical reference line. Now from the table we get various points to be plotted on the graph to obtain the line graph. So in the next step we plot the points 110. First we will plot this point that is the time is 1 minute and the temperature is 10 degrees Celsius. So now since the time is 1 minute so from 0 we will move one unit to the right we reach at this point. Now from here we will move 10 units up so that we get the temperature of 10 degrees Celsius. So this is the point that we obtain. This point is 110. Now next point to be plotted would be 235 that is the temperature at 2 minutes is 35 degrees Celsius. For this we will move 2 units to the right from 0. So we reach at this point and from here we move 35 units up so that we reach at the temperature 35 degrees Celsius that is we reach at this point. This point is 235. Now from the table we get the other point as 345 that is the temperature at 3 minutes would be 45 degrees Celsius and to plot this point we move 3 units to the right from the point 0 that is we reach at this point and from here we move 45 units up so as to reach at the temperature 45 degrees Celsius. So we reach at this point and this point is 345. Now the next point that we have to plot is 460 that is the temperature at 4 minutes is 60 degrees Celsius and to plot this point we move 4 units to the right from the point 0 so we reach at this point and from here we move 60 units up so as to reach at the temperature 60 degrees Celsius that is we get this point and this is 460. The next point that we have to plot would be 575 that is the temperature at 5 minutes is 75 degrees Celsius and to plot this point we move 5 units to the right from 0 so we reach at this point and from here we move 75 units up so as to reach at this point which shows that the temperature at 5 minutes is 75 degrees Celsius and this is the point 575. Now we have plotted all the points. Now we will join the successive points by the line segments to obtain the required line graph or the temperature time graph. So this is the required temperature time graph. Now next we are supposed to estimate the temperature of the water at t equal to 3.5 minutes. On this graph this is the point that depicts 3.5 minutes. Now we have to estimate the temperature of the water at 3.5 minutes. So from this point that is the point which shows 3.5 minutes we draw a line parallel to this vertical reference line to intersect this line graph. So we have drawn this line this line intersects the line graph at this particular point. Now from this point we will draw a line parallel to the horizontal reference line to intersect the vertical reference line. So we have drawn this line which is intersecting the vertical reference line at this point and this point is 52 degrees Celsius. Thus we get the temperature at 3.5 minutes is 52 degrees Celsius. So we can write from the line graph the temperature of the water at t equal to 3.5 minutes is 52 degrees Celsius. So we have drawn the line graph and also we have got the temperature of the water at t equal to 3.5 minutes which is 52 degrees Celsius. So this completes the session hope you have enjoyed the session have a good day.